What were its subdivisions? Were posts hereditary? Was it centralized or more of a tributary system? I couldn't find much information on each of these on the internet.
We have piecemeal information from historical and archaeological sources. It changed over time from a loosely organized hegemonic power to a centralized state with a large bureaucracy.
Before the Empire
Prior to the formation of the empire, P'urépecha governments were organized around units roughly equivalent to city-states. The indigenous term, according to Gilberti (1983) is ireta, and the ruler was known as the irecha. Each ireta was composed of smaller units variously called "barrios," wards, districts, or neighborhoods. The indigenous term for these units was uapátzequa (singular), or uapatzéquecha (plural) (Gilberti 1983; Van Zantwijk 1967). The uapátzequa was a political unit below the larger city-state government that included both nobles and commoners. Membership in them was likely hereditary (it is among modern P'urépecha, see Van Zantwijk 1967). Lesser levels of the nobility may have been heads of the uapanéquecha. A key insight made by some colonial administrators in the Relaciones Geográficas is that the P'urépecha, like the Aztecs, may not have differentiated between rural and urban components of city-states. So a uapátzequa may be a neighborhood within a city, or a suburb, or a completely separate town on the outskirts of the city's territory. Regardless, each had its own local council that managed local affairs such as marriages between residents or land disputes.
Smaller informal subdivisions likely also existed within the larger neighborhood-level units. Additionally, there were also likely some form of trade guilds that managed the production of certain crafts like stone masons and the weaving of reed mats. These kinds of organizations exist today within modern P'urépecha villages (Van Zantwijk 1967), and there are similar organizations implied in the Relacion de Michoacán (Acalá 2013).
The ruling dynasty of each ireta was inherited patrilineally. The royal lineage claimed much of their authority from control over sacred religious idols of the city's patron deity (Beltrán 1982). The actual position of Irecha was likely elected among the dynasty's heirs (Beltrán 1982). As depicted in the Relacion de Micoacán (Acalá 2013), the second most powerful ruler of the city was the petámuti or high priest. The priesthood was also hereditary (Warren 1985) and had their own bureaucracy, although the relationship between the priesthood and neighborhood institutions is poorly understood.
The Early Tarascan Empire
Some time during the 14th century AD, the city of Pátzcuaro conquered the other cities in the Lake Pátzcuaro Basin and formed what might be best thought of as a tributary empire. The Uanacaze dynasty, from a tribe of Chichimecs known as the Uacúsecha, deposed and eliminated many of the competing dynasties and placed members of their dynasty on the thrones of three key city-states. These cities established tributary hegemony over the lake basin and surrounding region. Taríacuri (the founder) had placed each of his three heirs Hiripan, Tangaxoan, and Hiquingaje in charge of Ihuatzio, Tzintzuntzan, and Pátzcuaro respectively (Acalá 2013). This early empire was likely a very fractious political arrangement. With some irony, it probably wasn't that different from the early Aztec Triple Alliance of Tenochtitlan, Texcoco, and Tlacopan. Local political groups were likely granted a large degree of autonomy. Haskell (2013) actually argues that the Early Empire never really had control over the lake basin and instead relied on peripheral conquests to secure power in local politics. I'm not completely sold on that argument. but it's worth considering. The early empire likely resembled the tributary model seen elsewhere in Mesoamerica during the early part of its history more than it did at the time of Spanish contact.
The ruler of the Tarascan Empire continued to use the title of Irecha (king) among P'urépecha language speakers. However, an additional title was added in diplomatic communications with the Aztecs: Caltzontzin, or (probably) "Lord of Four Hundred Houses" (Warren 1985).
In 1454 (following Pollard's 1993 chronology), a mysterious conflict ensued upon the death emperor Hiquíngaje that may or may not have involved a civil war. A recently translated P'urépecha-language document published by Monzón and colleagues (2009) indicates that the subsequent emperor, Tzitzispandáquare took the capital city of Tzintzuntzan by force. There are painfully few details on why this happened, but it's possible there was some kind of war of succession and/or rebellion after the last of the appointed successors of Taríacuri died.
The Late Tarascan Empire
After Tzitzispándaquaré's accession to the throne the structure of the empire changed dramatically. A series of dramatic political reforms were enacted to reduce the ability of conquered peoples to rebel. Local nobility within some conquered provinces were replaced with leaders appointed by Tzintzuntzan from among more loyal ethnic groups (Acalá 2013), and all matters of succession among any vassals of the emperor were settled by the emperor. The actual provincial nobles were known now as the caracha-capacha (demoted from irecha). The emperor further usurped the ability of nobles to use marriage to make alliances. All daughters of nobles were sent to the emperor's palace in Tzintzuntzan when they came of age, and he would marry them off to other lords (Beltrán 1982, Acalá 2013). Special tributary lands were set aside for the monarch in many conquered towns and cities, and farming or hunting on these lands without the King's permission was a serious offense.
As was true for pre-imperial P'urépecha polities, the Tarascan Empire's second in command continued to be the Petamuti (or high priest). There was also a group of officials described in the Relación de Michoacán (Acalá 2013) as the "Governors of the Four Quarters." Ostensibly, the empire was divided into four parts based on the cardinal directions centered on the capital Tzintzuntzan. Yet in practice, we have virtually know idea what these governors did on a day-to-day basis (Beltrán 1982). Their role may have been critical or purely ceremonial. There was also a group of nobles known as the Achaecha (a general term for noble) that followed the monarch around at all times (Acalá 2013). These were likely members of various advisory councils, although they may have been provincial lords.
A separate tributary bureaucracy, the ocámbecha, now managed the collection of taxes directly from the population instead of taking tribute from the city's government. According to the Relación de Michoacán (Acalá 2013), these officials were at some point assigned to units of 25 households, which would mean they also bypassed the authority of the neighborhood uapátzequa organization. In addition to collecting taxes, they also took census.
The emperor also appears to have "nationalized" the trade guilds. The Relación de Michoacán describes how the head of various crafting guilds were typically hereditary but that the monarch officially appointed them, much like the provincial nobility (Acalá 2013, Beltrán 1982).
Conclusion
By the time of the arrival of the Spanish the Tarascan Empire was a highly centralized, bureaucratized state, but this was largely a result of reforms later in the empire's history. For much of the history of the empire, this was not the case. The empire instead began as a loose hegemonic collection of city-states with multi-level subdivisions within city-states. The Tarascan Empire managed to build it's centralized bureaucracy by co-opting existing political arrangements and creating a dependency between local institutions and the monarchy.
Sources:
Acalá, Gerónimo de. 2013 [1540]. Relación de las ceremonias y ritos y poblacion y gobierno de los indios de la provincia de Michoacán.
Beltrán, Ulises. 1982. Tarascan State and Soceity in Prehispanic Times: An Ethnohistorical Inquiry. PhD Dissertation, University of Chicago.
Gilberti, Fray Maturino. 1983 [1559] Vocabulario en la lengua Mechuacan Compuesto por el reverendo padre Fray Maturino Gilberti de la ordé del Seráfico Padre San Francisco. Balsal Editores. Morelia Michoacan.
Haskell, David. L. 2013. Tarascan Historicity: Narrative Structure and the Production of the Past in the Case of the Two Tariacuris. Ethnohistory. 60 (4). pp. 637-662.
Monzón, Cristina; Hans Roskamp, and J. Benedict Warren. 2009. La Memoria de Don Melchor Caltzin (1543): Historia y Legitimación en Tzintzuntzan, Michoacan. Estudios de Historia Novohispana. (40). pp. 22-55.
Pollard, Helen. 1993. Tariacuri's Legacy: The Prehispanic Tarascan State. University of Oklahoma Press. Norman.
Relaciones geográficas de las diócesis de Michoacán, 1579-1580. Ed. José Corona Núñez (1958). Guadalajara, Mexico.
Van Zantwijk, Rudolf A. M. 1967. Servants of the Saints: The Social and Cultural Identity of a Tarascan Community in Mexico. Van Gorcum & Company N. V., Assen, Netherlands.
Warren, J. Benedict. 1985. The Conquest of Michoacan: Spanish Domination of the Tarascan Kingdom 1521-1530. University of Oklahoma Press, Norman.